## anonymous 5 years ago What mathematical induction?

1. anonymous

series of natural numbers

2. anonymous

But, I no get (k+1) part

3. amistre64

proving that if its true for one step; its true for every step

4. anonymous

for me you have to identify whta is the successor of 1, and it is 0, so 1 is the successor of k

5. anonymous

oops sorry

6. anonymous

So, if n=1 is true, then (k+1) should be true?

7. anonymous

No.

8. amistre64

you havent really asked that detailed of a question; youre keeping secrets

9. anonymous

The series of natural numbers, can all be defined if we know what we mean by the three terms "0," "number", and "successor." But we may go a step farther: we can define all the natural numbers if we know what we mean by "0" and "successor." It will help us to understand the difference between finite and infinite to see how this can be done, and why the method by which it is done cannot be extended beyond the finite. We will not yet consider how "0" and "successor" are to be defined: we will for the moment assume that we know what these terms mean, and show how thence all other natural numbers can be obtained.

10. watchmath

Have you seen a domino effect? that's how you should think about induction.

11. anonymous

Oops, didn't know you needed example. I sorry :) I give you example :) One moment, please

12. anonymous

1 + 2 + 3 + . . . + n = ½n(n + 1)

13. anonymous

The logic is: It's true for n= (for example) 1 AND you can prove truth for n=k implies truth for n=k+1) THEN It's true for n = 1, 2, 3.....

14. amistre64

n(n+1) ------ ah yes 2

15. amistre64

gausses fame..

16. anonymous

[Oh fun fact that isn't why Gauss is famous]

17. watchmath

Translating INewton logic into domino logic: How to make all the domino fall. 1) Make sure the 1st domino fall. 2) Make sure that whenever the kth domino fall, the (k+1)th domino fall as well. If you can ensure that then all dominos will fall :).

18. amistre64

n=2; 1+2 = 3 ; 2(2+1)/2 = 3

19. anonymous

............ THAT GREAT IDEA!!!!! :DDDDD

20. amistre64

its why I know gauss tho lol

21. amistre64

n = 3; 1+2+3 = 6 ; 3(3+1)/2 = 12/2 = 6

22. anonymous

Gauss Fact #1: Erdos believed God had a book of all perfect mathematical proofs. God believes Gauss has such a book.

23. anonymous

Gauss field equations

24. anonymous

Gauss Fact #2: Gauss checked the infinity of primes by counting them, starting from the last. Gauss Fact #3: Gauss considers infinity as the first non-trivial case in a proof by induction.

25. anonymous

$\text{Assume } \sum^k_{r=1}r = \frac{k(k+1)}{2}$ $\text{Assume } \sum^{k+1}_{r=1}r = \sum^k_{r=1}r + (k+1) = \frac{k(k+1)}{2} + (k+1) = \frac{k(k+1)+2(k+1)}{2}$ $=\frac{(k+1)[(k+1)+1]}{2}$ By mathematical induction blah...

26. watchmath

I think the second word of "assume" shouldn't be there.

27. anonymous

It shouldn't, lazy copy and past, ugh.... sorry.

28. anonymous

paste*. I should have used $\implies$ to start that line.